SOME GENERIC PROPERTIES OF NONLINEAR SECOND ORDER DIFFUSIONAL TYPE PROBLEM

Vladimir Durikovic and Maria Durikovicova

Address. Vladimir Durikovic, Department of Matematical Analysis of Komensky University

Mlynska dolina, 842 15 Bratislava, SLOVAK REPUBLIC

Maria Durikovicova, Department of Mathematics of Slovak Technical University

nam. Slobody 17, 800 01 Bratislava, SLOVAK REPUBLIC

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Abstract. We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij's decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem.

AMSclassification. 35K22, 47A53, 47F05, 47H15, 58G11

Keywords. Fredholm operator, H\"older space, bifurcation set, parabolic type operator, locally invertible operator